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arXiv · 1507.02089

Zero-free regions of partition functions with applications to algorithms and graph limits

Guus Regts
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Abstract

Based on a technique of Barvinok and Barvinok and Sober\'on we identify a class of edge-coloring models whose partition functions do not evaluate to zero on bounded degree graphs. Subsequently we give a quasi-polynomial time approximation scheme for computing these partition functions. As another application we show that the normalised partition functions of these models are continuous with respect the Benjamini-Schramm topology on bounded degree graphs. We moreover give quasi-polynomial time approximation schemes for evaluating a large class of graph polynomials, including the Tutte polynomial, on bounded degree graphs.

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Guus Regts. 2015-07-08. Zero-free regions of partition functions with applications to algorithms and graph limits. https://doi.org/10.1007/s00493-016-3506-7

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